I will go ahead and put my own anecdotes forward. I can attest that it is absolutely possible to have every dream be lucid. I have achieved 100% lucidity rates in the past and had maintained it for a good long while. It took a lot of focus and dedication at first but it eventually just became normal for me. I have also met a few other people who had achieved the same ability. And then of course there are the natural lucid dreamers who grow up thinking that everyone knows when they are dreaming because all the only dreams they ever experience are lucid.
In my experience, when I first started to achieve those high frequency rates of lucid dreams, I actually did not feel totally well rested. I would feel mentally exhausted after waking up, but I do not believe this was inherently due to the act of lucid dreaming. I was testing my limits and trying very hard to boost my frequency of lucid dreams and essentially placing stress on my mind from all the effort I put in. I just kept working at it though and eventually it became second nature and felt effortless. At that point I was lucid dreaming all the time and would wake up fully refreshed without any mental exhaustion. It just became natural. I guess what you can take away from this is that even if you did find lucid dreaming exhausting, you would eventually adjust and adapt to it.
The only other problem with the concept of lucid dreaming all the time is that you don't know if it's truly all the time if you don't recall every dream. But how do we even know if we have recalled every single dream of the night? It's just too difficult to quantify. And even beyond that, it actually is possible to have lucid dreams that you don't recall. There have been countless times where I would wake up in the morning and remember nothing. Then several hours later in the day I would encounter something that triggered my memory and end up recalling a dream that had been lucid. Lucid dreams are generally much more likely to be recalled than non-lucids but even the lucid ones are at risk of being forgotten.